Subgroups — #10685136

Order 768.

634 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×#4925	C₂	1	1	yes	maximal, characteristic
3	C₂×#4924	C₂	1	1	yes	maximal, characteristic
4	#67711	C₂	1	4	yes	maximal, complemented
5	#8001	—	3	1	no	maximal, Sylow
6	C₂²×C₃×M₁₆	—	2	1	no	—
7	C₂²×C₃×C₄²	C₂²	1	1	yes	characteristic
8	C₂²×#208	—	2	1	no	—
9	C₃×#423	—	2	1	no	—
10	C₃×#423	—	2	1	no	—
11	C₃×#423	C₄	1	2	yes	—
12	C₃×#423	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊C₈	—	2	1	no	—
14	C₂×C₃×C₄⋊C₈	C₄	1	2	yes	—
15	C₂×#830	C₄	1	2	yes	—
16	#4925	—	2	1	no	—
17	#4925	—	2	1	no	—
18	#4925	—	2	1	no	—
19	#4925	—	2	1	no	—
20	#4924	—	2	1	no	—
21	#4924	—	2	1	no	—
22	#4924	C₄	1	2	yes	—
23	#4924	C₂²	1	2	yes	—
24	C₂×C₄⋊(C₃⋊C₈)	—	2	1	no	—
25	C₂×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	—
26	C₂×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
27	C₂×C₄×C₃⋊C₈	C₄	1	2	yes	—
28	C₂×#431	—	3	1	no	—
29	C₂×#423	—	3	1	no	—
30	C₂×#423	D₃	1	1	yes	characteristic
31	#1292	—	3	4	no	—
32	C₂³×C₃×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₃×C₄	D₄	1	1	yes	characteristic
34	C₂³×C₃×C₄	Q₈	1	1	yes	characteristic
35	C₂×C₃×M₁₆	—	2	2	no	—
36	C₂×C₃×M₁₆	—	2	2	no	—
37	C₂×C₃×M₁₆	—	4	2	no	—
38	C₂×C₃×M₁₆	—	4	2	no	—
39	C₂²×C₃×C₈	—	2	2	no	—
40	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄²	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
47	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
49	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄²	Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
52	C₂×#208	—	2	2	no	—
53	C₂×#208	—	2	2	no	—
54	C₂×#208	—	4	2	no	—
55	C₂×#208	—	4	2	no	—
56	C₂²×C₃⋊C₈	—	2	2	no	—
57	C₂²×C₃⋊C₈	C₂×C₄	1	4	yes	—
58	C₃×C₄⋊C₈	—	2	2	no	—
59	C₃×C₄⋊C₈	—	2	2	no	—
60	C₃×C₄⋊C₈	—	2	2	no	—
61	C₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
62	#830	—	2	2	no	—
63	#830	—	2	2	no	—
64	C₄⋊(C₃⋊C₈)	—	2	2	no	—
65	C₄⋊(C₃⋊C₈)	—	2	2	no	—
66	C₄⋊(C₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₃⋊C₈)	—	2	2	no	—
68	C₄⋊(C₃⋊C₈)	—	2	2	no	—
69	C₄⋊(C₃⋊C₈)	C₂×C₄	1	4	yes	—
70	C₄×C₃⋊C₈	—	2	2	no	—
71	C₄×C₃⋊C₈	—	2	2	no	—
72	C₂²×M₁₆	—	2	1	no	—
73	C₂²×M₁₆	—	6	1	no	—
74	C₂²×C₄²	C₂×D₃	1	1	yes	characteristic
75	#431	—	6	1	no	—
76	#431	—	6	1	no	—
77	#431	—	6	1	no	—
78	#431	—	6	1	no	—
79	#423	—	2	1	no	—
80	#423	—	2	1	no	—
81	#423	—	3	2	no	—
82	#423	—	3	2	no	—
83	#423	—	6	1	no	—
84	#423	—	6	1	no	—
85	#423	Dic₃	1	2	yes	—
86	#423	C₂×D₃	1	2	yes	—
87	C₂×C₄⋊C₈	—	2	1	no	—
88	C₂×C₄⋊C₈	—	3	2	no	—
89	C₂×C₄⋊C₈	—	3	2	no	—
90	C₂×C₄⋊C₈	—	6	1	no	—
91	C₂×C₄⋊C₈	Dic₃	1	2	yes	—
92	C₂×C₂²⋊C₈	—	3	2	no	—
93	C₂×C₄×C₈	—	3	2	no	—
94	C₂⁴×C₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×C₃×C₄	—	4	2	no	—
96	C₂²×C₃×C₄	—	4	2	no	—
97	C₂²×C₃×C₄	C₄²	1	1	yes	characteristic
98	C₂²×C₃×C₄	C₄²	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
101	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×C₃×C₄	D₈	1	2	yes	—
113	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
114	C₂²×C₃×C₄	SD₁₆	1	2	yes	—
115	C₂²×C₃×C₄	Q₁₆	1	2	yes	—
116	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₃×C₄	C₂×Q₈	1	1	yes	characteristic
119	C₃×M₁₆	—	4	4	no	—
120	C₃×M₁₆	—	4	2	no	—
121	C₃×M₁₆	—	4	2	no	—
122	C₂×C₃×C₈	—	2	4	no	—
123	C₂×C₃×C₈	—	4	4	no	—
124	C₃×C₄²	C₄²	1	1	yes	characteristic
125	C₃×C₄²	C₄²	1	1	yes	characteristic
126	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
127	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
128	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
129	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
130	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
131	C₃×C₄²	C₂²⋊C₄	1	1	yes	characteristic
132	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
133	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
134	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
135	C₃×C₄²	C₄⋊C₄	1	1	yes	characteristic
136	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
137	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
138	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
139	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
140	#208	—	4	4	no	—
141	#208	—	4	2	no	—
142	#208	—	4	2	no	—
143	C₂×C₃⋊C₈	—	2	4	no	—
144	C₂×C₃⋊C₈	—	2	4	no	—
145	C₂×C₃⋊C₈	—	4	4	no	—
146	C₂×C₃⋊C₈	—	4	4	no	—
147	C₂³×C₄	Dic₆	1	1	yes	characteristic
148	C₂³×C₄	C₄×D₃	1	1	yes	characteristic
149	C₂³×C₄	#67	1	1	yes	characteristic
150	C₂×M₁₆	—	2	2	no	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	—	4	2	no	—
153	C₂×M₁₆	—	4	2	no	—
154	C₂×M₁₆	—	6	2	no	—
155	C₂×M₁₆	—	6	2	no	—
156	C₂×M₁₆	—	12	2	no	—
157	C₂×M₁₆	—	12	2	no	—
158	C₂²×C₈	—	2	2	no	—
159	C₂²×C₈	—	3	4	no	—
160	C₂²×C₈	—	6	2	no	—
161	C₂×C₄²	Dic₆	1	1	yes	characteristic
162	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
163	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
164	C₂×C₄²	C₄×D₃	1	1	yes	characteristic
165	C₂×C₄²	D₁₂	1	1	yes	characteristic
166	C₂×C₄²	D₁₂	1	1	yes	characteristic
167	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
168	C₂×C₄²	C₂×Dic₃	1	1	yes	characteristic
169	C₂×C₄²	#67	1	1	yes	characteristic
170	C₂×C₄²	#67	1	1	yes	characteristic
171	C₂×C₄²	#67	1	1	yes	characteristic
172	C₂×C₄²	C₂²×D₃	1	1	yes	characteristic
173	C₄⋊C₈	—	2	2	no	—
174	C₄⋊C₈	—	2	2	no	—
175	C₄⋊C₈	—	2	2	no	—
176	C₄⋊C₈	—	3	4	no	—
177	C₄⋊C₈	—	6	2	no	—
178	C₄⋊C₈	—	6	2	no	—
179	C₄⋊C₈	—	6	2	no	—
180	C₄⋊C₈	—	6	2	no	—
181	C₄⋊C₈	—	6	2	no	—
182	C₄⋊C₈	C₂×Dic₃	1	4	yes	—
183	C₂²⋊C₈	—	6	2	no	—
184	C₂²⋊C₈	—	6	2	no	—
185	C₄×C₈	—	6	2	no	—
186	C₄×C₈	—	6	2	no	—
187	C₂³×C₃	—	4	1	no	—
188	C₂³×C₃	—	4	1	no	—
189	C₂³×C₃	#95	1	1	yes	characteristic
190	C₂³×C₃	#95	1	1	yes	characteristic
191	C₂³×C₃	#106	1	2	yes	—
192	C₂³×C₃	#107	1	2	yes	—
193	C₂³×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	2	no	—
197	C₂×C₃×C₄	—	2	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	4	1	no	—
201	C₂×C₃×C₄	—	4	1	no	—
202	C₂×C₃×C₄	—	4	1	no	—
203	C₂×C₃×C₄	—	4	1	no	—
204	C₂×C₃×C₄	—	4	1	no	—
205	C₂×C₃×C₄	—	4	1	no	—
206	C₂×C₃×C₄	#95	1	1	yes	characteristic
207	C₂×C₃×C₄	#95	1	1	yes	characteristic
208	C₂×C₃×C₄	#95	1	1	yes	characteristic
209	C₂×C₃×C₄	#95	1	1	yes	characteristic
210	C₂×C₃×C₄	#95	1	1	yes	characteristic
211	C₂×C₃×C₄	#95	1	1	yes	characteristic
212	C₂×C₃×C₄	#102	1	2	yes	—
213	C₂×C₃×C₄	#102	1	2	yes	—
214	C₂×C₃×C₄	#102	1	2	yes	—
215	C₂×C₃×C₄	#102	1	2	yes	—
216	C₂×C₃×C₄	#103	1	2	yes	—
217	C₂×C₃×C₄	#103	1	2	yes	—
218	C₂×C₃×C₄	#103	1	2	yes	—
219	C₂×C₃×C₄	#103	1	2	yes	—
220	C₂×C₃×C₄	#106	1	2	yes	—
221	C₂×C₃×C₄	#107	1	2	yes	—
222	C₂×C₃×C₄	C₂×C₄²	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×SD₁₆	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×Q₁₆	1	1	yes	characteristic
232	C₃×C₈	—	4	4	no	—
233	C₃⋊C₈	—	4	4	no	—
234	C₃⋊C₈	—	4	4	no	—
235	C₂⁴	Dic₃⋊C₄	1	1	yes	characteristic
236	C₂²×C₄	—	4	2	no	—
237	C₂²×C₄	—	4	2	no	—
238	C₂²×C₄	C₄×Dic₃	1	1	yes	characteristic
239	C₂²×C₄	C₄×Dic₃	1	1	yes	characteristic
240	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
241	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
242	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
243	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
244	C₂²×C₄	Dic₃⋊C₄	1	1	yes	characteristic
245	C₂²×C₄	C₄⋊Dic₃	1	1	yes	characteristic
246	C₂²×C₄	C₄⋊Dic₃	1	1	yes	characteristic
247	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
248	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	#213	1	2	yes	—
252	C₂²×C₄	#214	1	2	yes	—
253	C₂²×C₄	#215	1	2	yes	—
254	C₂²×C₄	#216	1	2	yes	—
255	C₂²×C₄	#217	1	1	yes	characteristic
256	C₂²×C₄	#217	1	1	yes	characteristic
257	C₂²×C₄	C₂×Dic₆	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
259	C₂²×C₄	C₂×#67	1	1	yes	characteristic
260	M₁₆	—	4	4	no	—
261	M₁₆	—	4	2	no	—
262	M₁₆	—	4	2	no	—
263	M₁₆	—	12	4	no	—
264	M₁₆	—	12	2	no	—
265	M₁₆	—	12	2	no	—
266	C₂×C₈	—	2	4	no	—
267	C₂×C₈	—	4	4	no	—
268	C₂×C₈	—	6	4	no	—
269	C₂×C₈	—	6	4	no	—
270	C₂×C₈	—	12	4	no	—
271	C₂×C₈	—	12	4	no	—
272	C₄²	C₄×Dic₃	1	1	yes	characteristic
273	C₄²	C₄×Dic₃	1	1	yes	characteristic
274	C₄²	Dic₃⋊C₄	1	1	yes	characteristic
275	C₄²	Dic₃⋊C₄	1	1	yes	characteristic
276	C₄²	C₄⋊Dic₃	1	1	yes	characteristic
277	C₄²	C₄⋊Dic₃	1	1	yes	characteristic
278	C₄²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
279	C₄²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
280	C₄²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
281	C₄²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
282	C₄²	#217	1	1	yes	characteristic
283	C₄²	#217	1	1	yes	characteristic
284	C₄²	C₂×C₄×D₃	1	1	yes	characteristic
285	C₄²	C₂×D₁₂	1	1	yes	characteristic
286	C₄²	C₂²×Dic₃	1	1	yes	characteristic
287	C₄²	C₂×#67	1	1	yes	characteristic
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	4	2	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	#340	1	2	yes	—
297	C₂²×C₃	#340	1	2	yes	—
298	C₂²×C₃	C₂×#95	1	1	yes	characteristic
299	C₂²×C₃	C₂×#106	1	1	yes	characteristic
300	C₂²×C₃	C₂×#107	1	1	yes	characteristic
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	#338	1	2	yes	—
308	C₃×C₄	#340	1	2	yes	—
309	C₃×C₄	#340	1	2	yes	—
310	C₃×C₄	#413	1	2	yes	—
311	C₃×C₄	C₂×#102	1	1	yes	characteristic
312	C₃×C₄	C₂×#102	1	1	yes	characteristic
313	C₃×C₄	C₂×#103	1	1	yes	characteristic
314	C₃×C₄	C₂×#103	1	1	yes	characteristic
315	C₂³	—	4	1	no	—
316	C₂³	—	4	1	no	—
317	C₂³	#807	1	2	yes	—
318	C₂³	#808	1	2	yes	—
319	C₂³	C₃⋊#95	1	1	yes	characteristic
320	C₂³	C₃⋊#95	1	1	yes	characteristic
321	C₂³	C₂×Dic₃⋊C₄	1	1	yes	characteristic
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	1	no	—
330	C₂×C₄	—	4	1	no	—
331	C₂×C₄	—	4	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	#807	1	2	yes	—
335	C₂×C₄	#808	1	2	yes	—
336	C₂×C₄	#809	1	2	yes	—
337	C₂×C₄	#809	1	2	yes	—
338	C₂×C₄	#810	1	2	yes	—
339	C₂×C₄	#810	1	2	yes	—
340	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
342	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
343	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
344	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
345	C₂×C₄	C₃⋊#95	1	1	yes	characteristic
346	C₂×C₄	#832	1	2	yes	—
347	C₂×C₄	#832	1	2	yes	—
348	C₂×C₄	#835	1	2	yes	—
349	C₂×C₄	#835	1	2	yes	—
350	C₂×C₄	C₂×C₄×Dic₃	1	1	yes	characteristic
351	C₂×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
353	C₂×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
354	C₂×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×#213	1	1	yes	characteristic
356	C₂×C₄	C₂×#214	1	1	yes	characteristic
357	C₂×C₄	C₂×#215	1	1	yes	characteristic
358	C₂×C₄	C₂×#216	1	1	yes	characteristic
359	C₂×C₄	C₂×#217	1	1	yes	characteristic
360	C₈	—	4	4	no	—
361	C₈	—	12	4	no	—
362	C₈	—	12	4	no	—
363	C₂×C₃	—	2	2	no	—
364	C₂×C₃	—	2	2	no	—
365	C₂×C₃	—	2	1	no	—
366	C₂×C₃	—	2	1	no	—
367	C₂×C₃	C₂×#338	1	1	yes	characteristic
368	C₂×C₃	C₂×#340	1	1	yes	characteristic
369	C₂×C₃	#1742	1	1	yes	characteristic
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	#4529	1	2	yes	—
379	C₂²	#4529	1	2	yes	—
380	C₂²	C₂×#807	1	1	yes	characteristic
381	C₂²	C₂×#808	1	1	yes	characteristic
382	C₂²	C₂×C₃⋊#95	1	1	yes	characteristic
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	#4529	1	2	yes	—
390	C₄	#4529	1	2	yes	—
391	C₄	C₃⋊#338	1	2	yes	—
392	C₄	C₂×#809	1	1	yes	characteristic
393	C₄	C₂×#810	1	1	yes	characteristic
394	C₄	#5132	1	2	yes	—
395	C₄	C₂×#832	1	1	yes	characteristic
396	C₄	C₂×#835	1	1	yes	characteristic
397	C₃	#8001	1	1	yes	characteristic, complemented, Sylow
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	2	2	no	—
401	C₂	—	2	2	no	—
402	C₂	C₂×#4529	1	1	yes	characteristic
403	C₂	#71987	1	1	yes	characteristic
404	C₂	C₂×C₃⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₃⋊#95
commutator	C₂×C₃×C₄	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₃
Fitting	C₂×C₃×#423	C₂
socle	C₂²×C₃	C₂×#95
prime radical	C₂⁴×C₃	C₄⋊C₄
cosocle	C₂×C₃×C₄²	C₂³
hypercenter	C₂×#423	D₃
hypocenter	C₃	#8001
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#423

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. #67711	C₂	semidirect
397. C₃	#8001	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#423	2
C₂×#4925	2
C₂×#4924	2
#67711	2
#8001	3